The Energy System of Matter Part 6

[1] The conception of "Nature's Perfect Engine" was originally arrived at by the author from consideration of the phenomena of the steam-engine. The following extract from the "Review" of his work (1895) ill.u.s.trates the various stages which finally lead to that conclusion:--

"My first steps in the right direction came about thus. I had always been working with a cylinder and piston, and could make no progress, till at length it struck me to make my cylinder high enough to do without a piston--that is, to leave the steam to itself and observe its behaviour when left to work against gravity. The first thing I had to settle was the height of my cylinder. And I found, by calculation from Regnault's experiments that it would require to be very high, and that the exact height would depend on the temperature of the water in the boiler which was the bottom of this ideal cylinder. Now, at any ordinary temperature the height was so great that it was impossible to get known material to support its own weight, and I did not wish to use a hypothetical substance in the construction of this engine. Finally, the only course left me was to abolish the cylinder as I had done the piston. I then discovered that the engine I had been trying to evolve--the perfect engine--was not the ideal thing I had been groping after but an actual reality, in full working order, its operations taking place every day before my eyes.

"Every natural phenomenon fitted in exactly; it had its function to perform, and the performance of its function const.i.tuted the phenomenon. Let me trace the a.n.a.logy in a few of its details. The sea corresponds to the boiler; its cylinder surrounds the earth; it has for its fuel the axial energy of the earth; it has no condenser because it has no exhaust; the work it performs is all expended in producing the fuel. Every operation in the cycle is but an energy transformation, and these various transformations const.i.tute the visible life of the world."

[2] For definite numerical examples see the author's _Terrestrial Energy_ (Chap. 1.).

It will be evident, from a general consideration of this process of transmission of energy from the aqueous vapour, that relatively large quant.i.ties of that vapour are not required in the atmosphere for the working of the gaseous machine. The peculiar property of ready condensation of the aqueous vapour makes the evaporative process a continuous one, and the highly energised aqueous material, although only present in comparatively small amount, contributes a continuous flow of energy, and is thus able to steadily convey a very large quant.i.ty to the atmospheric ma.s.ses. For the same reason, the greater part of the energy transmission from the aqueous vapour to the air will take place at comparatively low alt.i.tudes and between reasonably high temperatures.

The working of any evaporative cycle may also be spread over very large terrestrial areas by the free movement of the acting material. Aqueous vapour rising in equatorial regions may finally return to the earth in the form of ice-crystals at the poles. In every complete cycle, however, the total expenditure per unit ma.s.s of material initially evaporated is always the latent heat at the higher or evaporation temperature; in the final or return stages of the cycle, any energy not transmitted to the air ma.s.ses is devoted to the heating of returning aqueous material.

Referring again to the transmitted energy, and speaking in the broadest fas.h.i.+on, the function of the aqueous vapour in the atmosphere may be likened to that of the steam in the cylinder of a steam-engine. In both cases the aqueous material works in a definite machine for energy transmission. In the case of the steam-engine work energy is transmitted (-- 31) from the steam through the medium of the moving piston and rotating shaft, and thence may be further diverted to useful purposes.

In the planetary atmospheric machine the work energy of aqueous vapour is likewise transmitted by the agency of the moving air ma.s.ses, not to any external agent, but back once more to its original source, which is the planetary axial energy. In neither case are we able to explain the precise nature of the transmission process in its ultimate details. We cannot say _how_ the steam transmits its work energy by the moving piston, nor yet by what agency the elevated particles of aqueous material transmit their energy to the air ma.s.ses. Our knowledge is confined entirely to the phenomena, and, fortunately, these are in some degree accessible. Nature presents direct evidence that such transmissions actually take place. This evidence is to be found, in both cases, in the condensation of the aqueous material which sustains the loss of its work energy. In the engine cylinder condensation takes place due to work being transmitted from the steam; in the atmosphere the visible phenomena of condensation are likewise the ever present evidence of the transmission of work energy from the aqueous vapour to the air ma.s.ses. In virtue of this accession of energy these ma.s.ses will, accordingly, be expanded upwards against the gravitational attractive forces. This upward movement, being made entirely at the expense of energy communicated from the aqueous vapour, is not accompanied by the normal fall of temperature due to the expansion of the air. Planetary axial energy, originally absorbed by the aqueous vapour, in the work form, has been transferred to the air ma.s.ses in the same form, and is now, after the expansive movement, resident in these ma.s.ses in the form of energy of position. It is the function of the atmospheric machine in its final stage to return this energy in the original axial form.

41. _Terrestrial Energy Return_

Let it be a.s.sumed that an atmospheric ma.s.s has been raised, by the transmission of work energy, to a high alt.i.tude in the equatorial regions of the earth. The a.s.sumption of locality is made merely for ill.u.s.trative purposes; it will be evident to the reader that the transmission of work energy to the atmospheric ma.s.ses and their consequent elevation will be continuously proceeding, more or less, over the whole planetary surface. To replace the gaseous material thus raised, a corresponding ma.s.s of air will move at a lower level, towards the equator from the more temperate zones adjoining. A circulatory motion will thus be set up in the atmosphere. In the upper regions the elevated and energised air ma.s.ses move towards the poles; at lower levels the replacing ma.s.ses move towards the equator, and in their pa.s.sage may be operated on by the aqueous vapour which they encounter, energised, and raised to higher levels. The movement will be continuous.

In their transference from equatorial towards polar regions, the atmospheric ma.s.ses are leaving the surfaces or regions of high linear velocity for those of low, and must in consequence lose or return in the pa.s.sage a portion of that natural energy of motion which they possess in virtue of their high linear velocity at the equator. But on the other hand, the replacing air ma.s.ses, which are travelling in the opposite direction from poles to equator, must gain or absorb a corresponding amount of energy. The one operation thus balances the other, and the planetary equilibrium is in no way disturbed. But the atmospheric ma.s.ses which are moving from the equator in the polar direction will possess, in addition, that energy of position which has been communicated to them through the medium of the aqueous vapour and by the working of the second stage of the atmospheric machine. These ma.s.ses, in the circulatory polar movements, move downwards towards the planetary surface. In this downward motion (as in the downward motion of a pendulum ma.s.s vibrating under the action of gravitation) the energy of position of the air ma.s.s is converted once more into energy of motion--that is, into its original form of axial energy of rotation. In equatorial regions the really important energy property of the atmospheric ma.s.s was indicated by its elevation or its energy of position. In the descent this energy is thus entirely transformed, and reverts once more to its original form of energy of rotation.

The continual transformation of axial energy by the aqueous vapour, and the conversion of that energy by the upward movement of the air ma.s.ses into energy of position, naturally tends to produce a r.e.t.a.r.dative effect on the motion of revolution of the earth. But this r.e.t.a.r.dative effect is in turn completely neutralised or balanced by the corresponding accelerative effect due to the equally continuous return as the energy of the air ma.s.ses reverts in the continuous polar movement to its original axial form. Speaking generally, the equatorial regions, or the regions of high velocity, are the location of the most powerful transformation or abstraction of axial energy by the aqueous vapour.

Conversely, the polar or regions of low velocity are the location of the greatest return of energy by the air. As no energy return is possible unless by the transference of the atmospheric material from regions of high to regions of low velocity, the configuration of the planet in rotation must conform to this condition. The spheroidal form of the earth is thus exquisitely adapted to the working of the atmospheric machine. As already pointed out, however, the energising and raising of atmospheric ma.s.ses is by no means confined to equatorial regions, but takes place more or less over the whole planetary surface. The same applies to the energy return. The complete cycle may be carried out in temperate zones; gaseous ma.s.ses, also, leaving equatorial regions at high alt.i.tudes do not necessarily reach the polar regions, but may attain their lowest levels at intermediate points. Neither do such ma.s.ses necessarily proceed to the regions of low velocity by purely linear paths. On the contrary, they may and do move both towards the poles and downwards by circuitous and even vortical paths. In fact, as will be readily apparent, their precise path is of absolutely no moment in the consideration of energy return.

It might naturally be expected that such movements of the atmospheric air ma.s.ses as have been described above would give rise to great atmospheric disturbance over the earth's surface, and that the transfer of gaseous material from pole to equator and vice versa would be productive of violent storms of wind. Such storms, however, are phenomena of somewhat rare occurrence; the atmosphere, on the whole, appears to be in a state of comparative tranquillity. This serenity of the atmosphere is, however, confined to the lower strata, and may be ascribed to an inherent stability possessed by the air ma.s.s as a whole in virtue of the accession of energy to it at high levels. As already explained, the transfer of energy from the vapour to the air ma.s.ses is accomplished at comparatively low alt.i.tudes, and when this reaction is taking place the whole tendency of the energised material is to move upwards. In so moving it tends to leave behind it the condensed aqueous vapour, and would, therefore, rise to the higher alt.i.tudes in a comparatively dry condition. This dryness is accentuated by the further loss of aqueous vapour by condensation as the air moves toward regions of low velocity. That air which actually attains to the poles will be practically dry, and having also returned, in its entirety, the surplus energy obtained from the aqueous vapour, it will be in this region practically in the condition of statical equilibrium of a gas against gravity (-- 34). But the general state of the atmosphere in other regions where a transference of energy from the aqueous vapour has taken or is taking place is very different from this condition of natural statical equilibrium which is approached at the poles. In the lower strata of the atmosphere the condition in some cases may approximate to the latter, but in the upper strata it is possessed of energy qualities quite abnormal to statical equilibrium. Its condition is rather one of the nature of stable equilibrium. It is in a condition similar to that of a liquid heated in its upper layers; there is absolutely no tendency to a direct or vertical downward circulation. In statical equilibrium, any downward movement of an air ma.s.s would simply be accompanied by the natural rise in temperature corresponding to the transformation of its energy of position, but in this condition of stable equilibrium any motion downwards must involve, not only this natural temperature rise, but also a return, either in whole or in part, of the energy absorbed from the aqueous vapour. The natural conditions are therefore against any direct vertical return. These conditions, however, favour in every respect the circulatory motion of the highly energised upper air ma.s.ses towards regions of low velocity. All circ.u.mstances combine, in fact, to confine the more powerfully energised and highly mobile air ma.s.ses to high alt.i.tudes. In the lower atmosphere, owing to the continuous action of the aqueous vapour on the air ma.s.ses moving from regions of low to those of high velocity, the circulation tends largely to be a vertical one, so that this locality is on the whole preserved in comparative tranquillity. It may happen, however, that owing to changes in the distribution of aqueous vapour, or other causes, this natural stability of the atmosphere may be disturbed over certain regions of the earth's surface. The circ.u.mstances will then favour a direct or more or less vertical return of the energy of the air ma.s.ses in the neighbourhood of these regions. This return will then take the form of violent storms of wind, usually of a cyclonic nature, and affording direct evidence of the tendency of the air ma.s.ses to pursue vortical paths in their movement towards lower levels.

Under normal conditions, however, the operation of the atmospheric machine is smooth and continuous. The earth's axial energy, under the sun's incepting influence, steadily flows at all parts of the earth's surface through the aqueous vapour into the atmospheric ma.s.ses, and the latter, rising from the terrestrial surface, with a motion somewhat like that of a column of smoke, spread out and speed towards regions of lower velocity, and travelling by devious and lengthened paths towards the surface, steadily return the abstracted energy in its original form.

Every operation is exactly balanced; energy expenditure and energy return are complementary; the terrestrial atmospheric machine as a whole works without jar or discontinuity, and the earth's motion of rotation is maintained with absolute uniformity.

Like every other energy machine, the atmospheric machine has clearly-defined energy limits. The total quant.i.ty of energy in operation is strictly limited by the ma.s.s of the acting materials. It is well, also, to note the purely mechanical nature of the machine. Every operation is in reality the operation of mechanical energy, and involves the movement of matter in some way or other relative to the earth's surface and under the incepting action of the earth's gravitation (---- 16, 20). The moving gaseous ma.s.ses have as real an existence as ma.s.ses of lead or other solid material, and require as real an expenditure of energy to move them relative to the terrestrial surface (-- 18). This aspect of the planetary machine will be more fully treated later.

Throughout this description we have constantly a.s.sumed the atmospheric mixture of oxygen and nitrogen to act as one gas, and at ordinary temperatures the respective energy properties of the two substances (-- 35) make this a.s.sumption justifiable. Both gases are then working far above their respective evaporation temperatures. But, in the higher regions of the atmosphere, where very low temperatures prevail, a point or alt.i.tude will be reached where the temperature corresponds to the evaporation or condensation temperature of one of the gases. Since oxygen appears to have the highest temperature of evaporation (see Table of Properties, p. 133), it would naturally be the first to condense in the ascent. But immediately condensation takes place, the material will become susceptible to the incepting influence of the sun, and working as it does at its temperature of evaporation it will convey its energy to the surrounding nitrogen in precisely the same fas.h.i.+on as the aqueous vapour conveys the energy to the aerial mixture in the lower atmosphere.

The whole action is made possible simply by the difference existing in the respective evaporation temperatures of the two gases. It will give rise to another cyclical atmospheric energy process exactly as already described for lower alt.i.tudes. Axial energy of rotation will be communicated to the nitrogen by the working material, which is now the oxygen, and by the movement of the nitrogen ma.s.ses towards regions of low velocity, this transmitted energy will be finally returned to its original axial form.

It has been already explained (---- 10, 32) how all terrestrial energy processes, also, great or small, are sooner or later linked to the general atmospheric machine. The latter, therefore, presents in every phase of its working completely closed energy circuits. In no aspect of its operation can we find any evidence of, or indeed any necessity for, an energy transmission either to or from any external body or agent such as the sun. Every phenomenon of Nature is, in fact, a direct denial of such transmission.

The student of terrestrial phenomena will readily find continuous and ample evidence in Nature of the working of the atmospheric machine. In the rising vapour and the falling rain he will recognise the visible signs of the operation of that great secondary process of transmission by which the inherent axial energy of the earth is communicated to the air ma.s.ses. The movements of bodies, animate and inanimate, on the earth's surface, the phenomena of growth and decay, and in fact almost every experience of everyday life, will reveal to him the persistent tendency of the energy of secondary processes to revert to the atmospheric machine. And in the winds that traverse the face of the globe he will also witness the mechanism of that energy return which completes the atmospheric cyclical process. It may be pointed out here also that the terrestrial cyclical energy processes are not necessarily all embodied in the atmosphere. The author has reason to believe, and phenomenal evidence is not awanting to show, that the circulatory motions of the atmosphere are in some degree reproduced in the sea. The reader will readily perceive that as regards stability the water composing the sea is in precisely the same condition as the atmosphere, namely, that of a liquid heated in its upper strata, and any circulatory motion of the water must therefore be accompanied by corresponding transformations of energy. That such a circulatory motion takes place is undoubted, and in the moving ma.s.s of sea-water we have therefore a perfectly reversible energy machine of the same general nature as the atmospheric machine, but working at a very much slower rate. It is not beyond the limits of legitimate scientific deduction to trace also the working of a similar machine in the solid material of the earth. The latter is, after all, but an agglomeration of loose material bound by the force of gravitation into coherent form. By the action of various erosive agencies a movement of solid material is continually taking place over the earth's surface. The material thus transported, it may be, from mountain chains, and deposited on the sea-bed, causes a disturbance of that gravitational equilibrium which defines the exact form of the earth. The forces tending to maintain this equilibrium are so enormous compared with the cohesive forces of the material forming the earth that readjustment continuously takes place, as evidenced by the tremors observed in the earth's crust. Where the structure of the latter is of such a nature as to offer great resistance to the gravitational forces, the readjustment may take the form of an earthquake. Geological evidence, as a whole, strongly points to a continuous kneading and flow of terrestrial material. The structure of igneous rocks, also, is exactly that which would be produced from alluvial deposits subjected during these cyclical movements to the enormous pressure and consequent heating caused by superimposed material. The occurrence of coal in polar regions, and of glacial residue in the tropics, may be regarded as further corroborative evidence. From this point of view also, it becomes unnecessary to postulate a genesis for the earth, as every known geological formation is shown to be capable of production under present conditions in Nature, and in fact to be in actual process of production at all times.

42. _Experimental a.n.a.logy and Demonstration of the General Mechanism of Energy Transformation and Return in the Atmospheric Cycle_

In the preceding articles, the atmospheric machine has been regarded more or less from the purely physical point of view. The purpose of this demonstration is now to place before the reader what might be termed the mechanical aspects of the machine; to give an outline, using simple experimental a.n.a.logies, of its nature and operation when considered purely and simply as a mechanism for the transformation and return of mechanical energy.

Familiar apparatus is used in ill.u.s.tration. In all cases, it is merely some adaptation of the simple pendulum (-- 21). Its minute structural details are really of slight importance in the discussion, and have accordingly been ignored, but the apparatus generally, and the energy operations embodied therein, are so familiar to physicists and engineers that the experimental results ill.u.s.trated can be readily verified by everyday experience. It is of great importance, also, in considering these results, to bear in mind the principles already enunciated (---- 13, 20) with reference to the operation of mechanical energy on the various forms of matter. The general working conditions of energy systems with respect to energy limits, stability, and reversibility (-- 23) should also be kept in view.

As an introductory step we shall review first a simple system of rotating pendulums. Two simple pendulums CM and DM{1} (Fig. 9) are mounted by means of a circular collar CD upon a vertical spindle AB, which is supported at A and B and free to rotate. When the central spindle AB is at rest the pendulums hang vertically; when energy is applied to the system, and AB is thereby caused to rotate, the spherical ma.s.ses M and M{1} will rise by circular paths about C and D.

This upward movement, considered apart from the centrifugal influence producing it, corresponds in itself to the upward movement of the simple pendulum (-- 21) against gravity. It is representative of a definite transformation, namely, the transformation of the work energy originally applied to the system and manifested in its rotary motion, into energy of position. The movements of the rotating pendulums will also be accompanied by other energy operations a.s.sociated with bearing friction and windage (---- 23, 29), but these operations being part of a separate and complete cyclical energy process (-- 32), they will in this case be neglected.

[Ill.u.s.tration: FIG. 9]

It will be readily seen, however, that the working of this rotating pendulum machine, when considered as a whole, is of a nature somewhat different from that of the simple pendulum machine in that the energy of position of the former (as measured by the vertical displacement of M and M{1} in rotation) and its energy of rotation must increase concurrently, and also in that the absolute maximum value of this energy of position will be attained when the pendulum ma.s.ses reach merely the horizontal level HL in rotation. The machines are alike, however, in this respect, that the transformation of energy of motion into energy of position is in each case a completely reversible process. In the working of the rotating pendulums the limiting amount of energy which can operate in this reversible process is dependent on and rigidly defined by the maximum length of the pendulum arms; the longer the arms, the greater is the possible height through which the ma.s.ses at their extremities must rise to attain the horizontal position in rotation. It will be clear also that it is not possible for the whole energy of the rotating system to work in the reversible process as in the case of the simple pendulum. As the pendulum ma.s.ses rise, the ratio of the limiting energy for reversibility to the total energy of the system becomes in fact smaller and smaller, until at the horizontal or position of maximum energy it reaches a minimum value. This is merely an aspect of the experimental fact that, as the pendulum ma.s.ses approach the ultimate horizontal position, a much greater increment of energy to the system is necessary for their elevation through a given vertical distance than at the lower levels. A larger proportion of the applied energy is, in fact, stored in the material of the system in the form of energy of strain or distortion.

The two points which this system is designed to ill.u.s.trate, and which it is desirable to emphasise, are thus as follows. Firstly, as the whole system rotates, the movement of the pendulum ma.s.ses M and M{1} from the lower to the higher levels, or from the regions of low to those of higher velocity, is productive of a transformation of the rotatory energy of the system into energy of position--a transformation of the same nature as in the case of the simple pendulum system. Neglecting the minor transformations (---- 24, 29), this energy process is a reversible one, and consequently, the return of the ma.s.ses from the higher to the lower positions will be accompanied by the complete return of the transformed energy in its original form of energy of rotation. Secondly, the maximum amount of energy which can work in this reversible process is always less than the total energy of the system. The latter, therefore, conforms to the general condition of stability (-- 25).

But this arrangement of rotating pendulums may be extended so as to include other features. To eliminate or in a manner replace the influence of gravitation, and to preserve the energy of position of the system--relative to the earth's surface--at a constant value, the pendulum arms may be a.s.sumed to be duplicated or extended to the points K and R (Fig. 10) respectively, where pendulum ma.s.ses equal to M and M{1} are attached.

The arms MK and M{1}R are thus continuous. Each arm is a.s.sumed to be pivoted at its middle point about a horizontal axis through N, and as the lower ma.s.ses M and M{1} rise in the course of the rotatory movement about AB the upper ma.s.ses K and R will fall by corresponding amounts.

The total energy of position of the system--referred to the earth's surface--thus remains constant whatever may be the position of the ma.s.ses in the system. The restraining influence on the movement of the ma.s.ses, formerly exercised by gravitation, is now furnished by means of a central spring F. A collar CD, connected as shown to the pendulum arms, slides on the spindle AB and compresses this spring as the ma.s.ses move towards the horizontal level HL. As the ma.s.ses return towards A and B the spring is released.

[Ill.u.s.tration: FIG. 10]

If energy be applied to the system, so that it is caused to rotate about the central axis AB, the pendulum ma.s.ses will tend to move outwards from that axis. Their movement may be said to be carried out over the surface of an imaginary sphere with centre on AB at N. The motion of the ma.s.ses, as the velocity of rotation increases, is from the region of lower peripheral velocity, in the vicinity of the axis AB, to the regions of higher velocity, in the neighbourhood of H and L. This outward movement from the central axis towards H and L is representative of a transformation of energy of an exactly similar nature to that described above in the simple case. Part of the original energy of rotation of the system is now stored in the pendulum ma.s.ses in virtue of their new position of displacement. But in this case, the movement is made, not against gravity, but against the central spring F. The energy, then, which in the former case might be said to be stored against gravitation (acting as an invisible spring) is in this case stored in the form of energy of strain or cohesion (-- 15) in the central spring, which thus as it were takes the place of gravitation in the system. As in the previous case also, the operation is a reversible energy process. If the pendulum ma.s.ses move in the opposite direction from the regions of higher velocity to those of lower velocity, the energy stored in the spring will be returned to the system in its original form of energy of motion.

A vibratory motion of the pendulums to and from the central axis would thus be productive of an alternate storage and return of energy. It is obvious also, that due to the action of centrifugal force, the pendulum ma.s.ses would tend to move radially outwards on the arms as they move towards the regions of highest velocity. Let this radial movement be carried out against the action of four radial springs S{1}, S{2}, S{3}, S{4}, as shown (Fig. 11). In virtue of the radial movement of the ma.s.ses, these springs will be compressed and energy stored in them in the form of energy of strain or cohesion (-- 15). The radial movement implies also that the ma.s.ses will be elevated from the surface of the imaginary sphere over which they are a.s.sumed to move. The elevation from this surface will be greatest in the regions of high velocity in the neighbourhood of H and L, and least at A and B. As the ma.s.ses move, therefore, from H and L towards the axis AB, they will also move inwards on the pendulum arms, relieving the springs, so that the energy stored in them is free to be returned to the system in its original form of energy of rotation. Every movement of the ma.s.ses from the central axis outwards against the springs is thus made at the expense of the original energy of motion, and every movement inwards provokes a corresponding return of that energy to the system. Every movement also against the springs forms part of a reversible operation. The sum total of the energy which works in these reversible operations is always less than the complete energy of the rotatory system, and the latter is always stable (-- 25), with respect to its energy properties. Let it now be a.s.sumed that the complete system as described is possessed of a precise and limited amount of energy of rotation, and that with the pendulum ma.s.ses in an intermediate position as shown (Fig. 11) it is rotating with uniform angular velocity. The condition of the rotatory system might now be described as that of equilibrium. A definite amount of its original rotatory energy is now stored in the central spring and also in the radial springs. If now, without alteration in the intrinsic rotatory energy of the system, the pendulum ma.s.ses were to execute a vibratory or pendulum motion about the position of equilibrium so that they move alternately to and from the central axis, then as they move inwards towards that axis the energy stored in the springs would be returned to the system in the original form of energy of rotation. This inward motion would, accordingly, produce acceleration. But, in the outward movement from the position of equilibrium, r.e.t.a.r.dation would ensue on account of energy of motion being withdrawn from the system and stored in the springs.

[Ill.u.s.tration: FIG. 11]

Under the given conditions, then, any vibratory motion of the pendulum ma.s.ses to and from the central axis would be accompanied by alternate r.e.t.a.r.dation and acceleration of the moving system. The storage of energy in the springs (central and radial) produces r.e.t.a.r.dation, the restoration of this energy gives rise to a corresponding acceleration.

The angular velocity of the system would rise and fall accordingly.

These are the natural conditions of working of the system. As already pointed out, the motion of the pendulum ma.s.ses may be regarded as executed over the surface of an imaginary sphere. Their motion against the radial springs would therefore correspond to a displacement outwards or upwards from the spherical surface. A definite part of the effect of r.e.t.a.r.dation is, of course, due to this outward or radial displacement of the ma.s.ses.

a.s.suming still the property of constancy of energy of rotation, let it now be supposed that in such a vibratory movement of the pendulum ma.s.ses as described above, the energy required merely for the displacement of the ma.s.ses _against the radial springs_ is not withdrawn from and obtained at the expense of the original rotatory energy of the system, but is obtained from some energy agency, completely external to the system, and to which energy cannot be returned. The r.e.t.a.r.dation, normally due to the outward displacement of the ma.s.ses against the radial springs, would not then take place. But the energy is, nevertheless, stored in the springs. It now, therefore, forms part of the energy of the system, and consequently, on the returning or inward movement of vibration of the ma.s.ses towards the central axis, this energy, received from the external source, would pa.s.s directly from the springs to the rotational energy of the system. It is clear, then, that while the introduction of energy in this fas.h.i.+on from an external source has in part eliminated the effect of r.e.t.a.r.dation, the accelerating effect must still operate as before. Each vibratory movement of the pendulum system, under the given conditions, will lead to a definite increase in its energy of rotation by the amount stored in the radial springs. If the vibratory movement is continuous, the rotatory velocity of the system will steadily increase in value. Energy once stored in the radial springs can only be released by the return movement of the ma.s.ses and _in the form of energy of rotation_; the nature of the mechanical machine is, in fact, such that if any incremental energy is applied to the displacement of the ma.s.ses against the radial springs, it can only be returned in this form of energy of motion.

These features of this experimental system are of vital importance to the author's scheme. They may be ill.u.s.trated more completely, however, and in a form more suitable for their most general application, by the hypothetical system now to be described. This system is, of course, devised for purely ill.u.s.trative purposes, but the general principles of working of pendulum systems and of energy return, as demonstrated above, will be a.s.sumed.

43. _Application of Pendulum Principles_

The movements of the pendulum ma.s.ses described in the previous article have been regarded as carried out over the surface of an imaginary sphere. Let us now proceed to consider the phenomena of a similar movement of material over the surface of an actual spherical ma.s.s. The precise dimensions of the sphere are of little moment in the discussion, but for the purpose of ill.u.s.tration, its ma.s.s and general outline may be a.s.sumed to correspond to that of the earth or other planetary body. This spherical ma.s.s A (Fig. 12) rotates with uniform angular velocity about an axis NS through its centre. a.s.sociated with the rotating sphere are four auxiliary spherical ma.s.ses, M{1}, M{2}, M{3}, M{4}, also of solid material, which are a.s.sumed to be placed symmetrically round its circ.u.mference as shown. These ma.s.ses form an inherent part of the spherical system; they are a.s.sumed to be united to the main body of material by the attractive force of gravitation in precisely the same fas.h.i.+on as the atmosphere or other surface material of a planet is united to its inner core (-- 34); they will therefore partake completely of the rotatory motion of the sphere about its axis NS, moving in paths similar to those of the rotating pendulum ma.s.ses already described (-- 42). The restraining action of the pendulum arms is, however, replaced in this celestial case by the action of gravitation, which is the central force or influence of the system. Opposite ma.s.ses are thus only united through the attractive influence of the material of the sphere.

The place of the springs, both central and radial, in our pendulum system is now taken by this centripetal force of gravitative attraction, which therefore forms the restraining influence or determining factor in all the a.s.sociated energy processes. While the auxiliary ma.s.ses M{1} M{2}, &c., partake of the general motion of revolution of the main spherical ma.s.s about NS, they may also be a.s.sumed to revolve simultaneously about the axis WE, perpendicular to NS, and also pa.s.sing through the centre of the sphere. Each of these ma.s.ses will thus have a peculiar motion, a definite velocity over the surface of the sphere from pole to pole--about the axis WE--combined with a velocity of rotation about the central axis NS. The value of the latter velocity is, at any instant, directly proportional to the radius of the circle of lat.i.tude of the point on the surface of the sphere where the ma.s.s happens to be situated at that instant in its rotatory motion from pole to pole; this velocity accordingly diminishes as the ma.s.s withdraws from the equator, and becomes zero when it actually reaches the poles of rotation at N and S; and the energy of each ma.s.s in motion, since its linear velocity is thus constantly varying, will be itself a continuously varying quant.i.ty, increasing or diminis.h.i.+ng accordingly as the ma.s.s is moving to or from the equatorial regions, attaining its maximum value at the equator and its minimum value at the poles. Now, since the ma.s.ses thus moving are a.s.sumed to be a material and inherent portion of the spherical system, the source of the energy which is thus alternately supplied to and returned by them is the original energy of motion of the system; this original energy being a.s.sumed strictly limited in amount, the increase of the energy of each ma.s.s as it moves towards the equator will, therefore, be productive of a r.e.t.a.r.dative effect on the revolution of the system as a whole. But, in a precisely similar manner, the energy thus gained by the ma.s.s would be fully returned on its movement towards the pole, and an accelerative effect would be produced corresponding to the original r.e.t.a.r.dation. In the arrangement shown (Fig. 12), the moving ma.s.ses are a.s.sumed to be situated at the extremities of diameters at right angles. With this symmetrical distribution, the transformation and return of energy would take place concurrently. r.e.t.a.r.dation is continually balanced by acceleration, and the motion of the sphere would, therefore, be approximately uniform about the central axis of rotation. It will be clear that the movements thus described of the ma.s.ses will be very similar in nature to those of the pendulum ma.s.ses in the experimental system previously discussed. The fact that the motion of the auxiliary ma.s.ses over the surface of the sphere is a.s.sumed to be completely circular and not vibratory, as in the pendulum case, has no bearing on the general energy phenomena. These are readily seen to be identical in nature with those of the simpler system. In each case every movement of the ma.s.ses implies either an expenditure of energy or a return, accordingly as the direction of that movement is to or from the regions of high velocity.

[Ill.u.s.tration: FIG. 12]

The paths of the moving auxiliary ma.s.ses have been considered, so far, only as parallel to the surface of the sphere, but the general energy conditions are in no way altered if they are a.s.sumed to have in addition some motion normal to that surface; if, for example, they are repelled from the surface as they approach the equatorial regions, and return towards it once more as they approach the poles. Such a movement of the ma.s.ses normal to the spherical surface really corresponds to the movement against the radial springs in the pendulum system; it would now be made against the attractive or restraining influence of gravitation, and a definite expenditure of energy would thus necessarily be required to produce the displacement. Energy, formerly stored in the springs, corresponds now to energy stored as energy of position (-- 20) against gravitation. If this energy is obtained at the expense of the inherent rotatory energy of the sphere, then its conversion in this fas.h.i.+on into energy of position will again be productive of a definite r.e.t.a.r.dative effect on the revolution of the system. It is clear, however, that if each ma.s.s descends to the surface level once more in moving towards the poles, then in this operation its energy of position, originally obtained at the expense of the rotatory energy of the sphere, will be gradually but completely returned to that source. In a balanced system, such as we have a.s.sumed above, the descent of one ma.s.s in rotation would be accompanied by the elevation of another at a different point; the abstraction and return of the energy of rotation would then be equivalent, and would not affect the primary condition of uniformity of rotation of the system. In the circ.u.mstances a.s.sumed, the whole energy process which takes place in the movement of the ma.s.ses from poles to equator and normal to the spherical surface would obviously be of a cyclical nature and completely reversible. It would be the working of mechanical energy in a definite material machine, and in accordance with the principles already outlined (-- 20) the maximum amount of energy which can operate in this machine is strictly limited by the ma.s.s of the material involved in the movement. The energy machine has thus a definite capacity, and as the maximum energy operating in the reversible cycle is a.s.sumed to be within this limit, the machine would be completely stable in nature (-- 25). The movements of the auxiliary ma.s.ses have hitherto also been considered as taking place over somewhat restricted paths, but this convention is one which can readily be dispensed with. The general direction of motion of the ma.s.ses must of course be from equator to pole or vice versa; but it is quite obvious that the exact paths pursued by the ma.s.ses in this general motion is of no moment in the consideration of energy return, nor yet the precise region in which they may happen to be restored once more to the surface level. Whatever may be its position at any instant, each ma.s.s is possessed of a definite amount of energy corresponding to that position; this amount will always be equal to the total energy abstracted by that ma.s.s, less the energy returned. The nature of the energy system is, however, such that the various energy phases of the different ma.s.ses will be completely co-ordinated. Since the essential feature of the system is its property of uniformity of rotation, any return of energy in the rotational form at any part of the system--due to the descent of material--produces a definite accelerating effect on the system, which effect is, however, at once neutralised or absorbed by a corresponding r.e.t.a.r.dative effect due to that energy which must be extracted from the system in equivalent amount and devoted to the upraising of material at a different point. For simplicity in ill.u.s.tration only four ma.s.ses have been considered in motion over the surface of the sphere, but it will be clear that the number which may so operate is really limited only by the dimensions of the system. The spherical surface might be completely covered with moving material, not necessarily of spherical form, not necessarily even material in the solid form (-- 13), which would rise and fall relative to the surface and flow to and from the poles exactly in the fas.h.i.+on already ill.u.s.trated by the moving ma.s.ses. The capacity of the reversible energy machine--which depends on the ma.s.s--would be altered in this case, but not the general nature of the machine itself.

If the system were energised to the requisite degree, every energy operation could be carried out as before.

As already pointed out, the dominating feature of a spherical system such as we have just described would be essentially its property of energy conservation manifested by its uniformity of rotation. All its operations could be carried out independently of the direct action of any external energy influences. For if it be a.s.sumed that the energy gained by the auxiliary moving surface material _in virtue of its displacement normal to the spherical surface_ be derived, not from the inherent rotational energy of the sphere itself, but by an influx of energy from some source completely external to the system, then since there has been no energy abstraction there will be no r.e.t.a.r.dative effect on the revolution due to the upraising of this material. But the influx of energy thus stored in the material must of necessity work through the energy machine. In the movement towards the poles this energy would therefore be applied to the system in the form of energy of rotation, and would produce a definite accelerative effect. If the influx of energy were continuous, and no means were existent for a corresponding efflux, the rotatory velocity of the system would steadily increase. The phenomena would be of precisely the same nature as those already alluded to in the case of the system of rotating pendulums (-- 42). Acceleration would take place without corresponding r.e.t.a.r.dation. A direct contribution would be continuously made to the rotatory energy of the system, and would under the given conditions be manifested by an increase in its velocity of revolution.

44. _Extension of Pendulum Principles to Terrestrial Phenomena_

The energy phenomena ill.u.s.trated by the experimental devices above are to be observed, in their aspects of greatest perfection, in the natural world. In the earth, united to its encircling atmosphere by the invisible bond of gravitation, we find the prototype of the hypothetical system just described. Its uniformity of rotation is an established fact of centuries, and over its spheroidal surface we have, corresponding to the motion of our ill.u.s.trative spherical ma.s.ses, the movement of enormous quant.i.ties of atmospheric air in the general directions from equatorial to polar regions and vice versa. This circulatory movement, and the internal energy reactions which it involves, have been already fully dealt with (-- 88); we have now to consider it in a somewhat more comprehensive fas.h.i.+on, in the light of the pendulum systems described above. As already explained (-- 13), the operation of mechanical energy is not confined to solid and liquid ma.s.ses only, but may likewise be manifested by the movements of gaseous ma.s.ses. The terrestrial atmospheric machine provides an outstanding example. In its working conditions, and in the general nature of the energy operations involved, the terrestrial atmospheric machine is very clearly represented by the rotating pendulum system (-- 42). The a.n.a.logy is still closer in the case of the hypothetical system just described. The actual terrestrial energy machine differs from both only in that the energy processes, which they ill.u.s.trate by the movements of solid material, are carried out in the course of its working by the motion of gaseous ma.s.ses. It is obvious, however, that this in no way affects the inherent nature of the energy processes themselves. They are carried out quite as completely and efficiently--in fact, more completely and more efficiently--by the motions of gaseous as by the motions of solid material.

The atmospheric circulation, then, may be readily regarded as the movement, over the terrestrial surface, of gaseous ma.s.ses which absorb and return energy in regions of high and low velocity exactly in the fas.h.i.+on explained above for solid material. In their movement from polar towards equatorial regions these ma.s.ses, by the action of the aqueous vapour (-- 38), absorb energy (axial energy) and expand upwards against gravity. Here we have an energy operation identical in nature with that embodied in the movements of a pendulum ma.s.s simultaneously over a spherical surface and against radial springs as in the system of rotating pendulums, or identical with the equatorial and radial movement of the auxiliary ma.s.ses in the hypothetical system. The return movement of the aerial ma.s.ses over the terrestrial surface in the opposite direction from equatorial to polar regions provides also exactly the same phenomena of energy return as the return movement of the ma.s.ses in our ill.u.s.trative systems. These systems, in fact, portray the general operation of mechanical energy precisely as it occurs in the terrestrial atmospheric machine. But obviously they cannot ill.u.s.trate the natural conditions in their entirety. The pa.s.sage or flow of the atmospheric air ma.s.ses over the earth's surface is a movement of an exceedingly complex nature, impossible to ill.u.s.trate by experimental apparatus. And indeed, such ill.u.s.tration is quite unnecessary. As already pointed out (-- 38), no matter what may be the precise path of an aerial ma.s.s in its movement towards the planetary surface the final energy return is the same.

Sooner or later its energy of position is restored in the original axial form.

The terrestrial atmospheric machine will be thus readily recognised as essentially a material mechanical machine corresponding in general nature to the ill.u.s.trative examples described above. The combination of its various energy processes is embodied in a complete cyclical and reversible operation. Its energy capacity, as in the simpler cases, is strictly limited by the total ma.s.s of the operating material. The active or working energy is well within the limit for reversibility (-- 23), and the machine is therefore essentially stable in nature. The continuous abstraction of axial energy by the aqueous vapour is balanced by an equally continuous return from the air ma.s.ses, and the system, so far as its energy properties are concerned, is absolutely conservative. Energy transmission from or to any external source is neither admissible nor necessary for its working.

45. _Concluding Review of Terrestrial Conditions--Effects of Influx of Energy_